Registers

1
Registers and Counters
Acknowledgement Most of the following slides are
adapted from Prof. Kale's slides at UIUC, USA.
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Registers and Counters

• Sequential circuits are classified based in their
  function, e.g., registers.
• Register A group of flip-flops each storing one
  bit of information.
• Registers include flip-flops and gates
  flip-flops hold the information, gates control
  how the information is transferred to the
  register.
• Counter is a register that goes through a
  predetermined sequence of states.

3
What good are registers?

• Flip-flops are limited because they can store
  only one bit.
• We had to use two flip-flops for our two-bit
  counter examples.
• Most computers work with integers and
  single-precision floating-point numbers that are
  32-bits long.
• Registers are commonly used as temporary storage
  in a processor.
• They are faster and more convenient than main
  memory.
• More registers can help speed up complex
  calculations.

Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
4
4-bit Register

• Loads in parallel
• Clear Cleans the output to all 0s.

Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
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Shift Registers
A register capable of shifting its binary
information in one or both directions is called
the shift register.
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
11
Serial transfer
Why do this? Maybe these are far apart
Could shift data in
Whats on wire at each clock?
Clocked 4 times
Slides adapted from Anselmo Lastra U. of North
Carolina at Chapel Hill
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Table Showing Shift

• A digital system is in the serial mode when
  information is processed one bit at a time.

Slides adapted from Anselmo Lastra U. of North
Carolina at Chapel Hill
13
Serial data transfer

• One application of shift registers is converting
  between serial data and parallel data.
• Computers typically work with multiple-bit
  quantities.
• ASCII text characters are 8 bits long.
• Integers, single-precision floating-point
  numbers, and screen pixels are up to 32 bits
  long.
• But sometimes its necessary to send or receive
  data serially, or one bit at a time. Some
  examples include
• Input devices such as keyboards and mice.
• Output devices like printers.
• Any serial port, USB or Firewire device transfers
  data serially.

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Receiving serial data

• To receive serial data using a shift register
• The serial device is connected to the registers
  SI input.
• The shift register outputs Q3-Q0 are connected to
  the computer.
• The serial device transmits one bit of data per
  clock cycle.
• These bits go into the SI input of the shift
  register.
• After four clock cycles, the shift register will
  hold a four-bit word.
• The computer then reads all four bits at once
  from the Q3-Q0 outputs.

serial device
computer
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Sending data serially

• To send data serially with a shift register, you
  do the opposite
• The CPU is connected to the registers D inputs.
• The shift output (Q3 in this case) is connected
  to the serial device.
• The computer first stores a four-bit word in the
  register, in one cycle.
• The serial device can then read the shift output.
• One bit appears on Q3 on each clock cycle.
• After four cycles, the entire four-bit word will
  have been sent.

computer
serial device
16
Remember 4-bit Parallel Adder Circuit?
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
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Serial Addition
Slower compared to parallel addition, but uses
less equipment.
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
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Serial Adder vs. Parallel Adder

• PA uses registers with parallel load, SA uses
  shift registers.
• PA uses more FAs compared to SA.
• Excluding the registers, PA is a combinational
  circuit, SA is sequential.

Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
19
Serial Adder Design Procedure

• State Table for a Serial Adder
• Present State Inputs Next State Output
  Flip-Flop inputs
• Q x y Q
  S J0 K0
• 0 0 0 0
  0 0 x
• 0 0 1 0
  1 0 x
• 0 1 0 0
  1 0 x
• 0 1 1 1
  0 1 x
• 1 0 0 0
  1 x 1
• 1 0 1 1
  0 x 0
• 1 1 0 1
  0 x 0
• 1 1 1 1
  1 x 0
• J0xy K0xy (xy)
  Sx XOR y XOR z

Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
20
Serial 4-bit Parallel Adder Circuit
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
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Serial vs. parallel pros and cons

• Serial vs. parallel adder
• One full adder vs. n adders
• Serial takes n units of time, parallel only one

Slides adapted from Anselmo Lastra U. of North
Carolina at Chapel Hill
23
Counters

• A register that goes trough a prescribed sequence
  of states is called a counter.
• Binary counter
• Counts through binary sequence
• n bit counter counts from 0 to 2n
• There are two groups of counters Ripple counters
  and Synchronous counters.
• Ripple counters The flip-flop output triggers
  other flip-flops.
• Synchronous counters count the clock.

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What good are counters?

• Counters can act as simple clocks to keep track
  of time.
• You may need to record how many times something
  has happened.
• How many bits have been sent or received?
• How many steps have been performed in some
  computation?
• All processors contain a program counter, or PC.
• Programs consist of a list of instructions that
  are to be executed one after another (for the
  most part).
• The PC keeps track of the instruction currently
  being executed.
• The PC increments once on each clock cycle, and
  the next program instruction is then executed.

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Binary Ripple Counter

• A binary ripple counter consists of a series of
  complementing flip-flops, with the output of each
  flip-flop connected to the next higher order.
• Examples of complementing flip-flops are T and D
  (with the output complement connected to the
  input) flip-flop.
• Binary Count Sequence
• A3 A2 A1 A0
• 0 0 0 0 A0 is complemented
  with each count pulse
• 0 0 0 1 A1 is complemented
  when A0 goes from 1 to 0
• 0 0 1 0 A2 is complemented
  when A1 goes from 1 to 0
• 0 0 1 1 A3 is complemented
  when A2 goes from 1 to 0
• 0 1 0 0
• 0 1 0 1
• 0 1 1 0
• 0 1 1 1
• 1 0 0 0

Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
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Examples of Binary Ripple Counters

• No clocks!
• Why is the Count is negated at the clock input?

count
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
27
Binary Ripple Counter

• Count-down counter A binary counter with reverse
  count Starts from 15 goes down.
• In a count-down counter the least significant bit
  is complemented with every count pulse. Any other
  bit is complemented if the previous bit goes from
  0 to 1.
• We can use the same counter design with negative
  edge flip-flops to make a count-down flip-flop.

Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
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BCD Ripple Counter
A BCD counter starts from 0 ends at 9.
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
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Logic Diagram of BCD Ripple Counter
Q1 is applied to the C inputs of Q2 and Q8 Q2 is
applied to the C input of Q4 J and K are
connected to either 1 or flip-flop outputs
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
30
Logic Diagram of BCD Ripple Counter

• Verification Does the circuit follow the states?
• Q1 is complemented with every count (JK1)?
• Q2 complements if Q1 goes from 1 to 0 and Q8 is 0
• Q2 remains 0 if Q8 becomes 1
• Q4 complements if Q2 goes from 1 to 0
• Q8 remains 0 as long as Q2 or Q4 is 0
• When Q2 and Q4 are 1, Q8 complements when Q1 goes
  from 1 to 0. Q8 clears and the next Q1 transition.

Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
31
Three-Decade Decimal BCD Counter
Counts from 0 to 999 When Q8 goes from 1 to 0
the next higher order decade is triggered
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
32
4-bit Synchronous Binary Counters
A flip-flop is complemented if all lower bits are
1.
A3 A2 A1 A0 0 0 0 0
0 0 0 1 0 0
1 0 0 0 1 1
0 1 0 0 0 1
0 1 0 1 1 0 0 1
1 1 1 0 0 0
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
33
4-bit Up-Down Binary Counters

• In a down binary counter
• a) The least significant bit is always
• complemented
• b) a bit is complemented if all lower
• bits are 0.

• Change an up counter to a down counter
• The AND gates should come from the
• complement outputs instead of the normal
• one

• Up 1, Down 0 Circuit counts up since
• input comes from Normal output

Up 0, Down 1 Circuit counts down since input
comes from Complemented output
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
34
Binary Counter with Parallel Load

• Sometimes we need an initial value prior to the
  count operation.
• Initial value I3 I2 I1 I0

Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
35
Binary Counter with Parallel Load
1
Count 1, Load 0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
36
Binary Counter with Parallel Load
0
Count 0, Load 1
0
1
0
1
I0
I0
1
0
I0
1
I1
I1
1
1
I1
1
I2
1
1
1
I2
1
I3
1
1
I3
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
37
BCD counter with parallel load

• In part a, 1001 (9) is detected. In part b, 1010
  (10) is detected. Why?
• In part a, LOAD is set to 1 and effective next
  cycle. (LOAD is a synchronous control input)
• In part b, counter is immediately cleared. (Clear
  is an asynchronous control input)?

Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
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Other Counters Ring Counter
A ring counter is a counter with ONLY 1 flip-flop
set to 1 at any particular time, all other are
cleared.
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
42
Other Counters Johnson Counter
A 4 flip-flop ring counter that produces 8 states
(not 4).
Slides adapted from Amirali Baniasadi amirali_at_ece.
uvic.ca
43
Registers - summary

• A register is a special state machine that stores
  multiple bits of data.
• Several variations are possible
• Parallel loading to store data into the register.
• Shifting the register contents either left or
  right.
• Counters are considered a type of register too!
• One application of shift registers is converting
  between serial and parallel data.
• Registers are a central part of modern
  processors, as we will see in coming weeks.

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Counters - Summary

• Counters serve many purposes in sequential logic
  design.
• There are lots of variations on the basic
  counter.
• Some can increment or decrement.
• An enable signal can be added.
• The counters value may be explicitly set.
• There are also several ways to make counters.
• You can follow the sequential design principles
  from last week to build counters from scratch.
• You could also modify or combine existing counter
  devices.

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RAM Random access memory

• Sequential circuits all depend upon the presence
  of memory.
• A flip-flop can store one bit of information.
• A register can store a single word, typically
  32-64 bits.
• Random access memory, or RAM, allows us to store
  even larger amounts of data.
• The basic interface to memory.
• How you can implement static RAM chips
  hierarchically.
• This is the last piece we need to put together a
  computer!

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Picture of memory

• You can think of computer memory as being one big
  array of data.
• The address serves as an array index.
• Each address refers to one word of data.
• You can read or modify the data at any given
  memory address, just like you can read or modify
  the contents of an array at any given index.
• If youve worked with pointers in C or C, then
  youve already worked with memory addresses.

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Size matters!

• Memory sizes are usually specified in numbers of
  bytes (8 bits).
• The 228-bit memory on the previous page
  translates into
• 228 bits / 8 bits per byte 225 bytes
• With the abbreviations below, this is equivalent
  to 32 megabytes.
• To confuse you, RAM size is measured in base 2
  units, while hard drive size is measured in base
  10 units.
• In this class, well only concern ourselves with
  the base 2 units.

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Typical memory sizes

• Some typical memory capacities
• PCs usually come with 256-4096MB RAM.
• PDAs have 64-512MB of memory.
• Digital cameras and MP3 players can have 512MB or
  more of storage.
• Many operating systems implement virtual memory,
  which makes the memory seem larger than it really
  is.
• Most systems allow up to 32-bit addresses. This
  works out to 232, or about four billion,
  different possible addresses.
• With a data size of one byte, the result is
  apparently a 4GB memory!
• The operating system uses hard disk space as a
  substitute for real memory.

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Static memory

• How can you implement the memory chip?
• There are many different kinds of RAM.
• Well start off discussing static memory, which
  is most commonly used in caches and video cards.
• Later we mention a little about dynamic memory,
  which forms the bulk of a computers main memory.
• Static memory is modeled using one latch for each
  bit of storage.
• Why use latches instead of flip flops?
• A latch can be made with only two NAND or two NOR
  gates, but a flip-flop requires at least twice
  that much hardware.
• In general, smaller is faster, cheaper and
  requires less power.
• The tradeoff is that getting the timing exactly
  right is a pain.

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Starting with latches

• To start, we can use one latch to store each bit.
  A one-bit RAM cell is shown here.
• Since this is just a one-bit memory, an ADRS
  input is not needed.
• Writing to the RAM cell
• When CS 1 and WR 1, the latch control input
  will be 1.
• The DATA input is thus saved in the D latch.
• Reading from the RAM cell and maintaining the
  current contents
• When CS 0 or when WR 0, the latch control
  input is also 0, so the latch just maintains its
  present state.
• The current latch contents will appear on OUT.

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My first RAM

• We can use these cells to make a 4 x 1 RAM.
• Since there are four words, ADRS is two bits.
• Each word is only one bit, so DATA and OUT are
  one bit each.
• Word selection is done with a decoder attached to
  the CS inputs of the RAM cells. Only one cell can
  be read or written at a time.
• Notice that the outputs are connected together
  with a single line!

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Connecting outputs together

• In normal practice, its bad to connect outputs
  together. If the outputs have different values,
  then a conflict arises.
• The standard way to combine outputs is to use
  OR gates or muxes.
• This can get expensive, with many wires and gates
  with large fan-ins.

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Those funny triangles

• The triangle represents a three-state buffer.
• Unlike regular logic gates, the output can be one
  of three different possibilities, as shown in the
  table.
• Disconnected means no output appears at all, in
  which case its safe to connect OUT to another
  output signal.
• The disconnected value is also sometimes called
  high impedance or Hi-Z.

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Connecting three-state buffers together

• You can connect several three-state buffer
  outputs together if you can guarantee that only
  one of them is enabled at any time.
• The easiest way to do this is to use a decoder!
• If the decoder is disabled, then all the
  three-state buffers will appear to be
  disconnected, and OUT will also appear
  disconnected.
• If the decoder is enabled, then exactly one of
  its outputs will be true, so only one of the
  tri-state buffers will be connected and produce
  an output.
• The net result is we can save some wire and gate
  costs. We also get a little more flexibility in
  putting circuits together.

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Bigger and better

• Here is the 4 x 1 RAM once again.
• How can we make a wider memory with more bits
  per word, like maybe a 4 x 4 RAM?
• Duplicate the stuff in the blue box!

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Getting to know Murphy

• Early in the '50s, with the advent of jet
  aircraft there was a debate as to whether a pilot
  could safely eject from the aircraft.  In order
  to find out whether a man could survive the
  stresses of ejection the Air Force undertook a
  study (USAF project MX981).  The study involved
  shooting a rocket sled down a track, accelerating
  its passenger to speeds in excess of 630 miles of
  hour and then suddenly stopping in 1.4 seconds,
  generating over 40g's.One experiment involved a
  set of 16 accelerometers mounted in different
  parts of the subject's body.  There were two ways
  each sensor could be glued to its mount.  And of
  course, each was installed the wrong way! One of
  the engineers on the project, Edward A. Murphy,
  made the original pronouncement of Murphy's Law,
  "If there are two or more ways to do something,
  and one of those can result in catastrophe, then
  someone will do it." The test subject, Major John
  Paul's Stapp an Air Force flight surgeon leading
  the project, quoted Murphy in a press conference
  a few days later.  Within months, Murphy's Law
  had spread to various technical cultures
  connected to aerospace engineering and finally to
  Webster's dictionary in 1958. excerpt taken
  from http//www.well.com/user/gjmurphy/Murphys_Law
  .html

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Error correction

• Murphys law "If anything can go wrong, it
  will!"
• Memory is no exception! Some bit will flip once
  in a while..
• Your task, of course if you accept it, is to
• Detect whether there is an error
• Correct it, if possible

• This slide will destroy itself in 5 seconds.

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Error-correction

• Use extra bits
• For instance append a parity bit
• For more interesting methods read the related
  section of the book.

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Summary

• A RAM looks like a bunch of registers connected
  together, allowing users to select a particular
  address to read or write.
• Much of the hardware in memory chips supports
  this selection process
• Chip select inputs
• Decoders
• Tri-state buffers
• By providing a general interface, its easy to
  connect RAMs together to make longer and
  wider memories.

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Other memories

• Some other kinds of memories.
• Dynamic RAM is used for the bulk of computer
  memory.
• Read-only memories and PLAs are two programmable
  logic devices, which can be considered as
  special types of memories.

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Dynamic memory in a nutshell

• Dynamic memory is built with capacitors.
• A stored charge on the capacitor represents a
  logical 1.
• No charge represents a logic 0.
• However, capacitors lose their charge after a few
  milliseconds. The memory requires constant
  refreshing to recharge the capacitors. (Thats
  whats dynamic about it.)?
• Dynamic RAMs tend to be physically smaller than
  static RAMs.
• A single bit of data can be stored with just one
  capacitor and one transistor, while static RAM
  cells typically require 4-6 transistors.
• This means dynamic RAM is cheaper and densermore
  bits can be stored in the same physical area.

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SDRAM

• Synchronous DRAM, or SDRAM, is one of the most
  common types of PC memory now.
• Memory chips are organized into modules that
  are connected to the CPU via a 64-bit (8-byte)
  bus.
• Speeds are rated in megahertz PC66, PC100 and
  PC133 memory run at 66MHz, 100MHz and 133MHz
  respectively.
• The memory bandwidth can be computed by
  multiplying the number of transfers per second by
  the size of each transfer.
• PC100 can transfer up to 800MB per second (100MHz
  x 8 bytes/cycle).
• PC133 can get over 1 GB per second.

(from amazon.com)?
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DDR-RAM

• A newer type of memory is Double Data Rate, or
  DDR-RAM.
• Its very similar to regular SDRAM, except data
  can be transferred on both the positive and
  negative clock edges. For 100-133MHz buses, the
  effective memory speeds appear to be 200-266MHz.
• This memory is confusingly called PC1600 and
  PC2100 RAM, because
• 200MHz x 8 bytes/cycle 1600MB/s
• 266MHz x 8 bytes/cycle 2100MB/s.
• DDR-RAM has lower power consumption, using 2.5V
  instead of 3.3V like SDRAM. This makes it good
  for notebooks and other mobile devices.

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RDRAM

• Another new type of memory called RDRAM is used
  in the Playstation 2 as well as some Pentium 4
  computers.
• The data bus is only 16 bits wide.
• But the memory runs at 400MHz, and data can be
  transferred on both the positive and negative
  clock edges.
• That works out to a maximum transfer rate of
  1.6GB per second.
• You can also implement two channels of memory,
  resulting in up to 3.2GB/s of bandwidth.

(from amazon.com)?
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Dynamic vs. static memory

• In practice, dynamic RAM is used for a computers
  main memory, since its cheap and you can pack a
  lot of storage into a small space.
• These days you can buy 2GB of memory for as
  little as 45TL.
• You can also load a system with 8GB or more of
  memory.
• The disadvantage of dynamic RAM is its speed.
• Transfer rates are 800MHz at best, which can be
  much slower than the processor itself.
• You also have to consider latency, or the time it
  takes data to travel from RAM to the processor.
• Real systems augment dynamic memory with small
  but fast sections of static memory called caches.
• Typical processor caches range in size from 2MB
  to 3MB.
• Thats small compared to a 2GB main memory, but
  its enough to significantly increase a
  computers overall speed.
• Youll study caches later on in CENG331 next
  semester.

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Memories and functions

• ROMs are actually combinational devices, not
  sequential ones!
• You cant store arbitrary data into a ROM, so the
  same address will always contain the same data.
• You can think of a ROM as a combinational circuit
  that takes an address as input, and produces some
  data as the output.
• A ROM table is basically just a truth table.
• The table shows what data is stored at each ROM
  address.
• You can generate that data combinationally, using
  the address as the input.

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Decoders

• We can already convert truth tables to circuits
  easily, with decoders.
• For example, you can think of this old circuit as
  a memory that stores the sum and carry outputs
  from the truth table on the right.

80
ROM setup

• ROMs are based on this decoder implementation of
  functions.
• A blank ROM just provides a decoder and several
  OR gates.
• The connections between the decoder and the OR
  gates are programmable, so different functions
  can be implemented.
• To program a ROM, you just make the desired
  connections between the decoder outputs and the
  OR gate inputs.

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Programmable logic arrays

• A ROM is potentially inefficient because it uses
  a decoder, which generates all possible minterms.
  No circuit minimization is done.
• Using a ROM to implement an n-input function
  requires
• An n-to-2n decoder, with n inverters and 2n
  n-input AND gates.
• An OR gate with up to 2n inputs.
• The number of gates roughly doubles for each
  additional ROM input.
• A programmable logic array, or PLA, makes the
  decoder part of the ROM programmable too.
  Instead of generating all minterms, you can
  choose which products (not necessarily minterms)
  to generate.

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PLA evaluation

• A k x m x n PLA can implement up to n functions
  of k inputs, each of which must be expressible
  with no more than m product terms.
• Unlike ROMs, PLAs allow you to choose which
  products are generated.
• This can significantly reduce the fan-in (number
  of inputs) of gates, as well as the total number
  of gates.
• However, a PLA is less general than a ROM. Not
  all functions may be expressible with the limited
  number of AND gates in a given PLA.
• In terms of memory, a k x m x n PLA has k address
  lines, and each of the 2k addresses references an
  n-bit data value.
• But again, not all possible data values can be
  stored.

91
Functions and memories

• ROMs and PLAs give us two more ways to implement
  functions.
• One difference between expressions/circuits and
  truth tables
• A circuit implies that some calculation has to be
  done on the inputs in order to arrive at the
  output. If the same inputs are given again, we
  have to repeat that calculation.
• A truth table lists all possible combinations of
  inputs and their corresponding outputs. Instead
  of doing a potentially lengthy calculation, we
  can just look up the result of a function.
• The idea behind using a ROM or PLA to implement a
  function is to store the functions truth
  table, so we dont have to do any (well, very
  little) computation.
• This is like memorization or caching
  techniques in programming.

92
Summary

• There are two main kinds of random access memory.
• Static RAM costs more, but the memory is faster.
  Static RAM is often used to implement cache
  memories.
• Dynamic RAM costs less and requires less physical
  space, making it ideal for larger-capacity
  memories. However, access times are also slower.
• ROMs and PLAs are programmable devices that can
  implement arbitrary functions, which is
  equivalent to acting as a read-only memory.
• ROMs are simpler to program, but contain more
  gates.
• PLAs use less hardware, but it requires some
  effort to minimize a set of functions. Also, the
  number of AND gates available can limit the
  number of expressible functions.